Which investment results in the greatest total amount?
Investment $A: \$ 5,000$ invested for 6 years compounded semiannually at $8 \%$. Investment B: $\$ 7,000$ invested for 3 years compounded quarterly at $3.6 \%$.
Find the total amount of investment $A$.
$\$ \square$ (Round to the nearest cent as needed.)

Step 1 ：Given that investment A is $5000 invested for 6 years compounded semiannually at 8%, we need to find the total amount of this investment.

Step 2 ：We use the formula for compound interest, which is \(A = P(1 + \frac{r}{n})^{nt}\), where: - A is the amount of money accumulated after n years, including interest. - P is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal). - n is the number of times that interest is compounded per year. - t is the time the money is invested for in years.

Step 3 ：For investment A, we have: - P = $5000 - r = 8% = 0.08 - n = 2 (since it's compounded semiannually) - t = 6 years.

Step 4 ：Substituting these values into the formula, we get: \(A = 5000(1 + \frac{0.08}{2})^{2*6}\)

Step 5 ：Solving this, we find that the total amount of investment A is approximately $8005.16.

Step 6 ：Final Answer: The total amount of investment A is \(\boxed{8005.16}\).